Question

A sample of 30 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 6. Conduct the following test of hypothesis using the 0.05 significance level. H0 : μ ≤ 20 H1 : μ > 20

Answer 1

Answer:

We conclude that μ <= 20 after hypothesis testing.

Step-by-step explanation:

We are given that sample of 30 observations is selected from a normal population.

Also, Sample mean, Xbar = 21 and Population Standard deviation, $\sigma$ = 6.

                  Null Hypothesis, $H_0$ : μ <=20

          Alternate Hypothesis, $H_1$ : μ > 20

So, Test Statistics we will use here is ;

                 $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ follows standard normal, N(0,1)

         Test statistics = $\frac{21 - 20}{\frac{6}{\sqrt{30} } }$ = 0.913 .

Now at 5% level of significance z % table gives the critical value of 1.6449 and our test statistics is less than this as 1.6449 > 0.913. So,we have sufficient evidence to do not reject null hypothesis or accept $H_0$ as our test statistics does not falls in the rejection region because it is less than 1.6449.

Hence we conclude after testing that Population mean, μ<=20.